I would go on 4 app schedule, early spring, late spring, early fall, late fall app of organic fertilizer. What fertilizer depends on lawn size and budget.

Weeds can be tricky. I know phasthound sells ADIOS, which is a sodium based product, but does have some restrictions. If you're not comfortable, find a local LCO to do weed control only apps, if you don't want to stay organic.